Ok so I am reading a book on linear algebra ( Gilbert Strang to be specific) and I am on second problem set, challenge problem, problem 29. In solutions it appears that the author states that:
$$x\cdot y=xz+yz+xy=(1/2)(x+y+z)^2 - (1/2)(x^2 + y^2 + z^2)$$
How is that possible?